Final answer:
The government debt would amount to $95 billion after a period of running a budget deficit of $10 billion annually for ten years, a surplus of $1 billion annually for five years, and a balanced budget for another ten years.
Step-by-step explanation:
To determine the government debt, we need to consider the net effect of budget surpluses and deficits over time. When the government runs a budget surplus, it means that it has earned more money than it has spent, which can be used to pay down the debt. Conversely, a budget deficit occurs when the government spends more than it earns, which increases the debt.
In this scenario, the government runs a budget deficit of $10 billion dollars each year for ten years. This adds up to a total deficit of $100 billion ($10 billion x 10 years). Afterward, the government runs a budget surplus of $1 billion for five years, which will reduce the debt by $5 billion ($1 billion x 5 years). Finally, with a balanced budget for another ten years, there are no further changes to the debt.
Considering these changes over time, the total government debt after this period would be $95 billion ($100 billion deficit - $5 billion surplus).